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PURPOSE OF ACTIVITYThe goal of this exercise is to enable students to explore some of the controls on fluid flow by having them simulate tur-bidity currents using lock-gate exchange tanks while vary-ing the bed slope and the turbidity. Observational data are compared with theoretical relationships known from the sci-entific literature. The exercise promotes collaborative/peer learning and critical thinking while using a physical model and analyzing results.

WHAT THE ACTIVITY ENTAILSDuring two lab periods of two and half hours duration, stu-dents use a physical model to simulate turbidity currents flow-ing over differing bottom slopes. They are given a Plexiglas tank and gate, a wooden stand to change the bottom slope, a drill with a paint stirring attachment to generate turbulence, sediment, rulers, and other equipment as described below. They determine how much sediment to add to vary the den-sity of the flow. The tank is filled with water of a known tem-perature (and thus known density and viscosity). The gate is inserted into the tank to provide a known volume of water in the lock behind the gate. While the drill is used to gener-ate turbulence in the lock, a known mass of sand is poured into the lock. The lock gate and drill are then removed, allow-ing the simulated turbidity current to flow down the tank. Students use smart phones or cameras to videotape and record the duration of the flow during the simulation. They record data needed to characterize the flows using sediment transport and basic fluid dynamics equations, and they write group reports of their findings. The simulations are con-ducted during the first lab period. The group analyzes the data during the second lab period and outside of class. The instructor and the teaching assistant are available to support the group learning experience during the lab periods, pro-viding assistance with the calculations and background on dimensional scaling.

LABORATORY INSTRUCTIONS AND WORKSHEET

Turbidity CurrentsComparing Theory and Observation in the Lab

By Joseph D. Ortiz and Adiël A. Klompmaker

DIMENSIONAL SCALING AS A MEANS OF COMPARING FLUID FLOWSWe can employ dimensional scaling to compare the prop-erties of various fluid flows. These provide a means of char-acterizing the flow from a theoretical standpoint. When the assumptions underlying these simple theories are met, the results match empirical observations. A current can pick up sediment off the bottom when the boundary shear stress (the force acting on the particle in the direction of the current) exceeds the drag on the particle. How the particle is trans-ported depends on its density, size, and the properties of the fluid flow. Larger particles are transported as bed load, roll-ing or scraping along the bottom. Smaller, less dense particles saltate (bounce along the bottom), and finer grains are trans-ported by suspension. The finest particles remain in suspen-sion the longest and are referred to as the wash load. The Rouse number relates the settling velocity of the particle to the boundary shear stress to estimate the manner of trans-port. The Reynolds number, the Froude number, and the Richardson number define the characteristics of the fluid flow. The Reynolds number can be used to determine the rel-ative importance of turbulence and laminar flow. The Froude number is used to determine if the flow is rapid or tranquil, and the Richardson number provides an estimate of the sta-bility of the flow, which in this context relates to how effec-tively the turbulence can be damped by the flow.

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BACKGROUND

Turbidity currents form one class of sediment gravity flows (e.g.,  Middleton, 1993). They are an important mechanism of sediment transport in fluid environments (lakes and the ocean) as they move coarse-grained material from the mar-gins to the interiors of basins. The ocean’s broad, flat abyssal plains are formed in part by the action of turbidity currents. Submarine canyons are carved by their repeated flow into the deep sea (Figure 1a).

Turbidity currents can be triggered by submarine failures such as a slumps and slides or by earthquakes or other dis-turbances such as storm-induced waves (e.g.,  Meiburg and Kneller, 2009). The supporting mechanism for the flow is turbulence. The current consists of sediment-laden, turbid water that travels downslope. As the sediment gravity flow

accelerates downslope, it scours the bottom, entraining fluid from above and sediment from below. The flow consists of a well-defined head, body, and tail.

A turbidite deposit forms as the sediment drops out of sus-pension or bedload transport ceases. Turbidites are compos-ite graded beds that include a variety of sedimentary struc-tures related to differences in the flow regime (Pickering et al., 1986). Turbidites are capped by thin drapes of silt or clay. Coarse, proximal turbidites, which are deposited near the ini-tiation points of turbidity currents, consist of thick beds of coarse-grained material over scoured bases. Intermediate-grained, medial turbidites are often expressed in the classic Bouma sequence (Figure 1b), consisting of scoured bases and several graded crossbeds sandwiched between thick basal

FIGURE 1. (a) Schematic of the marginal environment in marine and lacustrine settings where tur-bidity currents arise and turbidites are deposited (Source: Meiburg and Kneller, 2009). (b) Definition of the classic Bouma Sequence, one of several classification schemes that have been proposed for turbidite deposits. Note that proximal turbidites will exhibit coarser beds than distal turbidites, and not all beds in the Bouma sequence are present in all turbidite deposits (Source: Middleton, 1993).

b

sand and thinner silt or clay caps (Bouma, 1964; Bouma and Brouwer, 1964). Fine-grained, distal turbidite deposits exhibit smaller grain sizes and may lack high energy, cross-bedded fea-tures, making them difficult to differentiate from hemipelagic or pelagic sedimentation.

This laboratory exercise allows students to generate tur-bidity currents under con-trolled conditions using fine-grained sediment to create the turbidity that drives the trans-port (Figure  2). This activity provides a more concrete con-nection to the actual sediment transport and deposition of the flows observed in nature than simulations using water of dif-fering densities or colored with dye, or fluids of different densi-ties or viscosities (such as milk) to generate the turbid flow.

We can measure the veloc-ity of the flow empirically if we know the distance traveled per unit time:

Uobs = d t (1)

Considerable theoretical work has evaluated the factors that contribute to flow velocity (e.g., Middleton, 1993; Meiburg

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and Kneller, 2009; An, 2010). As the mass of sediment sus-pended in the flow increases, so does the density of the turbid flow relative to that of the ambient low-density water above it, and thus its velocity increases. We can estimate the flow velocity of the head using the theoretical relationship

Uhead = Fr – 1) ghρtρ( (2)

Notice that the flow velocity of the head is proportional to the density difference between the higher density, turbid, sediment- laden water in the flow (ρt in kg/m3) and the lower density, ambient water (ρ) multiplied by the acceleration of gravity (g in m/s2) and the height of the turbidity current (h in m). Prior research indicates the Froude number for the flow (Fr)—the ratio of inertial to gravitational forces acting on the flow—yields the proper coefficient of proportionality to relate the flow velocity to the density contrast (e.g., Kneller and Buckee, 2000).

The Froude number for a turbidity current is defined as

Fr = Uhead – 1) ghρtρ( (3)

where Uhead is the mean velocity of the turbid flow (in m s–1). When Fr is greater than 1, the flow is rapid, while for values less than 1, the flow is tranquil. Studies suggest

that appropriate Froude numbers for turbidity currents range between Fr = 2–1/2 to 1 for turbulent flow in deep water, while flows in finite water depth follow a relationship in which Fr h/H, where h is the height of the turbulent flow, and H is the water depth (e.g., Middleton, 1993; Meiburg and Kneller, 2009). In addition to the Froude number, the properties of turbidity currents can be described using three additional dimensionless numbers, the Reynolds number, the Rouse number, and the Richardson number.

The Reynolds (Re ) is a dimensionless number, which relates the turbulent forces driving the flow (numerator term) to the dissipative, frictional forces that diminish it (denomi-nator term). For Re greater than 2000, the flow is turbulent. For values less than 2000, the flow is laminar. The Re number is defined as

Re =ρtUhead h

µ (4)

where ρt is the density of the turbid fluid (in kg/m3), Uhead is the mean velocity of the head of the turbidity current (in m/s), h is the height of the turbidity current head, and µ is the dynamic (or molecular) viscosity of the water (in kg/ms), which depends on the temperature of the water. The viscosity and density of freshwater based on its temperature can be taken from a plot (Figure  3) or calculated from an

GEOMETRY OF THE TURBIDITY CURRENT TANK

Variables to measure:T = Water temperature ρ = Water density (determined based on temp)µ = Water viscosity (determined based on temp)Uhead = Flow velocity h = Average �ow height (measure at 75% of tank length)z = Height to maximum velocity (measure at 75% of tank length)H = Average water depth (measure at 75% of tank length)d = Distance traveled by current (from gate to 75% of tank length)t = Time for current to reach 75% of tank length (in seconds)s = Tank slope angle (in degrees)

NOTE:z will be muchsmaller than h

Removalof lock

z

h s

H Uhead

75% oftank

length

Distance (d) traveled by turbidity current in time (t)

Volume of turbid water in the lock based on its length (l), width (w), depth (Z), and

fraction (f) of the lock �lled with turbid water

FIGURE 2. Lab handout documenting tank geometry and variables to measure.

FIGURE 3. The temperature dependence of density and dynamic viscosity for freshwater. Values obtained from: http://www.mhtl.uwater-loo.ca/old/onlinetools/airprop/airprop.html.

1,001

1,000

999

998

997

996

995

0.0018

0.0016

0.0014

0.0012

0.0010

0.0008

0.0006

Den

sity

(kg

m–3

)

Visc

osity

(kg

m s

–1)

Temperature (°C)0 10 20 30

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online form (http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop/airprop.html). Given a measure of the water tem-perature, the form can be used to look up the density and vis-cosity of the freshwater in the tank. To calculate the density of the turbid, sediment-laden water, students need to account for the mass and volume of sediment added to the freshwater, which increases the density of the turbid mixture.

The Richardson number, which determines the stability of the flow, is defined as

Ri =2u2

*

– 1) gChρtρ( (5)

where C is the volume concentration of sediment in the flow (the ratio of the sediment volume to the volume of water in the lock), u* is the shear velocity of the flow (in m/s), and the other variables are as defined above. The shear velocity in this context is a measure of the rate of change of the velocity of the flow with distance from the bottom boundary, where friction causes the velocity to go to zero. This is the so-called “no slip” constraint. The shear velocity (u*) is defined as

u* = and τ = µ thus,ρt

τ∂z∂u

by substitution: ∂z∂uu* = ρt

µ

(6)

in which τ is the bottom boundary shear stress, a measure of the force acting on the sediment particles; ρt is the fluid den-sity of the turbulent flow (in kg/m3); μ is the dynamic vis-cosity of water (in kg/ms); and ∂u/∂z is the vertical velocity gradient, the rate of change of velocity with depth (in s–1). Without sophisticated equipment, measurements of ∂u/∂z and u* are difficult to quantify, but they can be measured with acceptable error. We can use the “no slip” assumption—which states that the velocity must be zero at the bottom boundary of the flow—in conjunction with the observed estimate of U to approximate ∂u. This will provide a crude, two-point esti-mate of the vertical velocity gradient from zero at the base of the flow to U, the observed mean velocity of the head. That provides the numerator, ∂u, for the vertical velocity gradi-ent. We will have to make an estimate of the depth where the velocity profile reaches the mean flow value. We will assume that it is equal to the flow height as it rides up over the clear water in front of the turbidity current to estimate ∂z based on our observation of the height of the leading edge of the head of the turbidity current, which we define as z. Thus, we can

estimate Ri and plot Ri vs. slope to see how they are related.With a description of the these flow characteristics, we also

can determine the manner in which sediment is transported by the turbid flow using the Rouse number, which relates the settling velocity of a grain to the shear boundary stress acting on it. The Rouse number P is defined as

P = κu*

ws (7)

where ws is the settling velocity of particles, κ is the von Kármán constant (generally taken as 0.41, see Gaudio et al., 2010), and u* is the shear velocity (in m/s), as described above. With a von Kármán constant of 0.41, a Rouse number <0.8 indicates “wash load” transport of very fine sediment. Values in the range of 0.8 to 1.2 indicate “suspended load” transport, values of 1.2 to 2.5 indicate that 50% of the transport is by suspen-sion, and values >2.5 indicate bedload transport (Dade and Friend, 1998; Udo and Mano, 2011).

For the settling velocity (ws in m/s), we will use the Impact Law, defined as

ws = 3Cd

4 – 1) gdρtρ( (8)

where Cd , is a drag coefficient, ρt is the density of the turbu-lent flow (in kg/m3), ρ is the density of the fluid (in kg/m3), g is the acceleration of gravity (in m/s2), and d is the diameter of an average spherical sediment particle (in m). To estimate Cd , we need to calculate a particle Reynolds number (Rep) in which the density and length scale are based on the proper-ties of the grain:

Rep =ρtwsdµ (9)

We can then determine the drag coefficient Cd for particles of specific shape from an empirical curve of Rep vs. Cd. This poses an immediate problem, however, because we see from Equation 9 that the Rep itself depends on ws, but we need to know Cd to determine ws using Equation 8. One solution to this problem is to iteratively solve for Rep by using initial esti-mates of Cd and ws and then to replace values of Cd and ws iteratively until the relationship converges on a solution with minimal errors in Cd. For operational purposes, we will define the convergence as a <10–4 difference in the initial and revised estimates of Cd. Once students know Cd and ws, they can deter-mine the Rouse number using Equation 7 (see also Figure 4).

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REFERENCESAn, R.-D., and J. Li. 2010. Characteristic analysis of the plunging of turbidity

currents. Journal of Hydrodynamics 22:274–282, http://dx.doi.org/ 10.1016/S1001-6058(09)60055-X.

Boggs, S. Jr. 2006. Principles of Sedimentology and Stratigraphy, 4th ed. Pearson Prentice Hall, Upper Saddle River, NJ, 662 pp.

Bouma, A.H. 1964. Ancient and recent turbidites. Geologie en Mijnbouw 43:375–379.

Bouma, A.H., and A. Brouwer, eds. 1964. Developments in Sedimentology 3: Turbidites. Elsevier, Amsterdam, 264 pp.

Cantero, M.I., A. Cantelli, C. Pirmez, S. Balachandar, D. Mohrig, T.A. Hickson, T.-H. Yeh, H. Naruse, and G. Parker. 2012. Emplacement of massive tur-bidites linked to extinction of turbulence in turbidity currents. Nature Geoscience 5:42–45, http://dx.doi.org/ 10.1038/ngeo1320.

Dade, W.B., and P.F. Friend. 1998. Grain-size, sediment-transport regime, and channel slope in alluvial rivers. The Journal of Geology 106:661–676, http://dx.doi.org/10.1086/516052.

Gaudio, R., A. Miglio, and S. Dey. 2010. Non-universality of von Kármán’s κ in flu-vial streams. Journal of Hydraulic Research 48:658–663, http://dx.doi.org/ 10.1080/00221686.2010.507338.

Kneller, B., and C. Buckee. 2000. The structure and fluid mechan-ics of turbidity currents: A review of some recent studies and their geological implications. Sedimentology 47:62–94, http://dx.doi.org/ 10.1046/j.1365-3091.2000.047s1062.x.

Meiburg, E., and B. Kneller. 2010. Turbidity currents and their deposits. Annual Review of Fluid Mechanics 42:135–156, http://dx.doi.org/10.1146/annurev-fluid-121108-145618.

Middleton, G.V. 1993. Sediment deposition from turbidity currents. Annual Review of Earth and Planetary Sciences 21:89–114, http://dx.doi.org/ 10.1146/annurev.ea.21.050193.000513.

Pickering, K., D. Stow, M. Watson, and R. Hiscott. 1986. Deep-water facies, pro-cesses and models: A review and classification scheme for modern and ancient sediments. Earth-Science Reviews 23:75–174, http://dx.doi.org/ 10.1016/0012-8252(86)90001-2.

Spalding, H.L., K.M. Duncan, and Z. Norcross-Nu’u. 2009. Hands-on oceanography: Sorting out sediment grain size and plastic pollution. Oceanography 22(4):244–250, http://dx.doi.org/ 10.5670/oceanog.2009.117.

Udo, K., and A. Mano. 2011. Application of Rouse’s sediment concentration pro-file to aeolian transport: Is the suspension system for sand transport in air the same as that in water? The Journal of Coastal Research 64 (Proceedings of the 11th International Coastal Symposium):2,079–2,083, http://www.cerf-jcr.org/images/stories/2011_ICS_Proceedings/SP64_2079-2083_K._Udo.pdf.

AUTHORSJoseph Ortiz (jortiz@kent.edu) is a professor in the Department of Geology at Kent State University, OH, USA. He holds a Ph.D. in Oceanography from the College of Earth, Ocean, and Atmospheric Sciences at Oregon State University. Adiël Klompmaker is a post-doctoral fellow at the Florida Museum of Natural History and affiliated faculty member in the Department of Geological Sciences, both at the University of Florida, FL, USA. He received his Ph.D. in Applied Geology from Kent State University.

FIGURE 4. (a) The relationship between ws and grain size under the Impact law with pure and turbid water and under Stokes law. (b) The relationship between the log10-transformed drag coefficient (Cd) and the log10-transformed particle Reynolds number (Rep ) plotted as blue-filled squares. The red-filled squares depict an approximation for the drag coefficient applicable for Stokes settling law, Rep ~ 24/Cd. The black curve provides a fourth-order, least-squares polyno-mial fit between the log-transformed Cd and Rep data: y = –4.56 x 10–3(x4) + 4.24 x 10–2(x3) + 2.59 x 10–2(x2) – 9.54 x 10–1(x) + 1.49.

0.30

0.25

0.20

0.15

0.10

0.05

0.00

3.0

2.5

2.0

1.5

1.0

0.5

0.0

–0.5

–1.0

Ws

(m s

–1)

Log 10

(Cd)

Log10(Rep)0.0 2.0

a b

–2.0 4.0 6.0Grain Size (mm)

0.0 0.4 0.8 1.2 1.6 2.00 8 1 2 1 6 2 0

Impact law (m s–1)with pure waterImpact law (m s–1)with turbid waterStokes law (m s–1)

Log(Cd)Log(24/Cd)Poly. (Log(Cd))

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CRITICAL THINKING QUESTIONS

The students should consider the following questions as they analyze their results. They should read the paper by Cantero et al. (2012) to help answer some of the research questions.

All Students (Equations 1–6)

1. How closely does the observed velocity of the turbidity current follow the theoretical relationships based on the Froude number? If the results are different, how can this be explained?

2. How might the results change if saltwater were used instead of freshwater?

3. How will the results vary as grain size is increased?

4. Which variables are likely to introduce the greatest error into each equation?

5. Do the turbidity currents generated in the lab follow the Ri scaling function of 1/S described in Cantero et al. (2012)? If the results are different, how can this be explained?

Grad Students (Equations 7–9)

6. What is the settling velocity of the average-sized grain in the turbidity current and what is the mode of sediment transport by the turbidity current using the Rouse number?

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MATERIALS

• Turbidity current tank (1.20 m long, 0.30 m tall, and 0.12 m wide)

• Gate (0.35 m tall by 0.12 m wide)

• Grease pens or erasable whiteboard markers to mark the sides of the tanks

• Stand to change the slope of the tank from 0° to 2°, 4°, and 6°

• Sediment with a known size distribution (i.e., determined using sieve analysis or an automated tool, such as a Malvern Mastersizer 2000)

• Scoop

• Plastic bag to hold sediment while measuring mass

• Drill equipped with a stirring apparatus to power the current

• Rulers, protractors, and meter sticks

• Scale

• Buckets for sand and water

• Thermometer

• Stopwatch (or phone with timer function)

• Still and video cameras

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ACTIVITY

1. During the first lab period, a short description of the project tasks is provided after which groups are formed (~30 min).

2. Students are asked to develop their procedural design to measure the parameters needed and to determine the constants needed to answer the research questions (~20 minutes).

3. Their plan will be discussed with the professor and TA.4. Materials are provided to perform the simulation after

which the tank will be filled with water followed by a test run to become familiar with the method. Tasks will be divided within each team (~15 minutes).

5. Simulations will be carried out, making sure to collect the data listed below (2–3 hours). The tank is emptied and cleaned between simulations, with the sand saved in a bucket and dried for future use. Groups generally complete between 2 and 4 runs during a lab period of 2½ hours.

6. Before the second lab period, students are asked to read the article by Cantero et al. (2012) after which a class discus-sion follows (~30 minutes).

7. During the second lab period, the groups can work on cal-culations and report writing. Include an introduction, a methods section, results, discussion, conclusion, and what could be changed if you had the opportunity to do the sim-ulation again. Videos can be uploaded to an ftp space or dropbox (1–2 weeks following the lab).

Each group will need to measure or estimate the following for each simulation:

Prior to Simulation1. Slope of tank measured in degrees (°) with a protractor or

determined trigonometrically: slope % = 100*(rise/run), then convert to slope (°) = atan*(slope %/100).2. Mass of sediment added (determine the sediment volume

based on assumed density of quartz. Remember to con-vert units. You should use a sediment mass concentration (mass of sediment divided by mass of water in the lock) in the range between 25 and 350 g/L.

3. Water temperature (to get water density [ρ], molecular vis-cosity [μ], and the mass of water in the lock based on its density and volume), see Equation 4.

4. Dimensions of the lock behind the gate to determine the initial volume of turbid water so that they can estimate the density of turbid water: ρt = (sediment mass + water mass)/(sediment volume + water volume).

5. Water depth in the tank, H.

During Simulation1. Height of turbidity current, h.2. Time s in seconds to reach a specific constant distance, d

(from this, we get: Uobs = d/s).3. Height above the bottom of the leading edge of the turbid-

ity current, z.

After Simulation1. Calculate U empirically as: Uobs = d/s.2. Use Uobs, μ, ρt, and z to estimate u* from Equation 6.3. Compare Uobs with the theoretical relationships for Uhead

from Equation 2 and calculate values for each of the other equations. Calculate residuals (Ures = Uobs – Uhead) to esti-mate the difference between theory and observation.

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TURBIDITY CURRENT DATA COLLECTION SHEETUse this sheet to collect the data you will need to calculate the experimental results.

Constants Value (m)

Tank length (m)

Tank width (m)

Tank height (m)

Sediment density 2,650 kg m–3

Acceleration of gravity (m/s2) 9.81

von Kármán constant 0.41

Variables to measure Run #1 Run #2 Run #3 Run # 4

Length of lock gate (m)

Water depth at midpoint behind lock gate (m)

Water depth at measurement point located at 75% of tank length (H; m)

Slope of tank (°)

Average particle grain size (m)

Distance traveled by turbidity current to measurement point at 75% of tank length (m)

Time for turbidity current to travel to measurement point at 75% of tank length (s)

Temperature of water (°C)

Use temp to took up density of water (kg m–3)

Use temp to look up dynamic viscosity of water (kg/ms)

Mass of sediment added (kg)

Volume of water in lock (kg)

Mass of water in lock (kg)

Mass of turbid water (kg; mass of water plus mass of sediment)

Volume of water in lock (m3)

Volume of sediment in lock (m3; obtain from sediment mass and density)

Density of turbid water ( ρt, kg m–3)

Height of turbidity current (h; m)

Height of leading edge of turbidity current (z; m)

Volume concentration of particles (volume of sediment divided by volume of water in lock). Use this value in Equation 5

Mass concentration of sediment (mass of sediment divided by volume of water in lock). Use this concentration to evaluate mass of sediment to add: should be between 25 and 350 g L–1.